(Solved): It was shown in class that the wavefunction of a particle confined in an infinite potential well, ...

It was shown in class that the wavefunction of a particle confined in an infinite potential well, in a 1-D space having a width (a) (i.e., \( \mathrm{U}=\infty \) for \( \mathrm{x} \leq 0 \) and \( \mathrm{x} \geq \mathrm{a} \); and \( \mathrm{U}=0 \) for \( 0<\mathrm{x}<\mathrm{a}) \), is given by: \[ \psi(\mathrm{x})=\mathrm{A} \sin (\mathrm{kx}) \] where \( \mathrm{k}=\mathrm{n} \pi / \mathrm{a}, \mathrm{n} \) is an integer and \( \mathrm{A} \) is a coefficient. Using the fourth postulate, i.e. the integral of the probability of finding the particle over all space (from \( -\infty \) to \( +\infty) \) is equal to 1 , determine the coefficient \( \mathrm{A} \) as a function of the width (a) of the potential well.